Abstract
It has been known for more than a century that, counter to one’s intuition, the frequency of occurrence of the first significant digit in a very large number of numerical data sets is nonuniformly distributed. This result is encapsulated in Benford’s law, which states that the first (and higher) digits follow a logarithmic distribution. An interesting consequence of the counter intuitive nature of Benford’s law is that manipulation of data sets can lead to a change in compliance with the expected distribution—an insight that is exploited in forensic accountancy and financial fraud. In this investigation we have applied a Benford analysis to the distribution of price paid data for house prices in England and Wales pre and post-2014. A residual heat map analysis offers a visually attractive method for identifying interesting features, and two distinct patterns of human intervention are identified: (i) selling property at values just beneath a tax threshold, and (ii) psychological pricing, with a particular bias for the final digit to be 0 or 5. There was a change in legislation in 2014 to soften tax thresholds, and the influence of this change on house price paid data was clearly evident.
Highlights
Introduction9 to occur in the first index in a number drawn from many real-world data sets is not uniform [1]
Benford’s first digit law Benford’s first-digit law— known as the Newcomb–Benford law, or the law of anomalous numbers—describes the counter intuitive phenomenon that the probability of the digits 1, 2, . . . , 9 to occur in the first index in a number drawn from many real-world data sets is not uniform [1]
The Fibonacci numbers, which appear in the growth patterns of sunflowers, pinecones and other plants and flowers [3]
Summary
9 to occur in the first index in a number drawn from many real-world data sets is not uniform [1]. Over half a century later, Benford analysed 20 datasets, including the values of physical constants and population data, for conformity with Newcomb’s findings. Extensive numerical data sets exist that display non-uniform distribution of the first digit. The Fibonacci numbers are more likely to start with one than any other digit, with nine the least likely digit to appear. The Fibonacci numbers are said to follow Benford’s law [4] which quantifies this property. Numerous data sets that arise in different scientific disciplines have been found—to differing quantitative extents—to conform with Benford’s law. An extensive database of articles, books and other resources related to Benford’s law can be found at [15]
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